Grouping of Identical Cells

Series Grouping

In a series grouping of N cells, current in the external circuit is l. The polarity of how many cells should be reversed so that the current becomes (1/3)rd of the earlier value?

Solution:

Before reversing the polarity of the cells, the current is

l = NE / R + Nr

Let n cells be reversed in their polarity.

\ Net emf = (N – n)E – nE = (N – 2n) E

Total resistance NR + R

Þ i’ = (N – 2n)E / Nr + R

But, 1' / 1 = (N–2n)E / (R + Nr) / (NE / Nr + R) = N – 2n / N

Þ n = N/3,

This is valid only when N is a multiple of 3, otherwise it cannot be done.

Parallel Grouping

Let there be n identical rows each containing a cell of emf e

and a resistance r arranged as shown in the figure.

Alt txt : parallel grouping

Applying Kirchhoff’s law

e–1/ n r – lR = 0Þ l = nz / r + nR

* To get maximum current, cells must be connected in series if effective internal resistance is less than external resistance and in parallel if effective internal resistance is greater than external resistance.